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residence inn las vegas convention center by marriott las vegas - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 Substitute \(x\) into the first equation: \(2(43/14) + 3y = 16\).

📌 Simplify: \(86/14 + 3y = 16\), or \(3y = 16 - 43/7\).

📌 Convert: \(3y = 112/7 - 43/7 = 69/7\).

📌 Solve for \(y\): \(y = 69 / 21 = 23/7\).

📌 #### \(x = 43/14\), \(y = 23/7\)

📌 The sum of the first \(n\) terms of an arithmetic sequence is given by \(S_n = \frac{n}{2}(2a + (n-1)d)\). Find the sum of the first 5 terms if \(a = 3\) and \(d = 2\).

📌 Substitute the values: \(S_5 = \frac{5}{2}(2 \times 3 + 4 \times 2)\).

📌 Simplify: \(S_5 = \frac{5}{2}(6 + 8) = \frac{5}{2} \times 14 = 35\).

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Adding these two expressions:
Simplify by combining like terms:
= 2\sin^2 x + 2\cos^2 x = 2(\sin^2 x + \cos^2 x)
Using the Pythagorean identity \(\sin^2 x + \cos^2 x = 1\):
= 2 \times 1 = 2
Therefore, the maximum value is \(\boxed{2}\).
Find the value of \(x\) such that the vectors \(\begin{pmatrix} \sin x...
Two vectors are orthogonal if their dot product is zero. Let’s compute...
\begin{pmatrix} \sin x \\ \cos x \end{pmatrix} \cdot \begin{pmatrix} \...
The dot product is always zero, regardless of \(x\). Hence, the vector...

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